Jamieson, Fausset and Brown on Hebrews 7:15

15. Another proof that the law, or economy, is changed, namely, forasmuch as Christ is appointed Priest, "not according to the law of a carnal (that is, a mere outward) commandment," but "according to the power of an indissoluble (so the Greek) life." The hundred tenth Psalm appoints Him "for ever" (He 7:17). The Levitical law required a definite carnal descent. In contrast stands "the power"; Christ's spiritual, inward, living power of overcoming death. Not agreeably to a statute is Christ appointed, but according to an inward living power.

it--the change of the law or economy, the statement (He 7:12, 18).

far more--Greek, "more abundantly."

for that--"seeing that," literally, "if"; so Ro 5:10.

after the similitude of Melchisedec--answering to "after the order of Melchisedec" (He 5:10). The "order" cannot mean a series of priests, for Melchisedec neither received his priesthood from, nor transmitted it to, any other mere man; it must mean "answering to the office of Melchisedec." Christ's priesthood is similar to Melchisedec's in that it is "for ever" (He 7:16, 17).

another--rather as Greek, "a different."